Transcript Shape Forming by Cutting and Deforming Operations Koichi Hirota

Shape Forming by Cutting
and Deforming Operations
Koichi Hirota, Atsuko Tanaka, Toyohisa Kaneko, Michitaka Hirose
Proc. ICAT 2000, 19-24, 2000.10
9217005 黃琬婷
2007.1.2
OUTLINE
Introduction
 Deformation Operation
 Tearing Operation
 Cutting Operation
 Conclusion

Introduction

GOAL
Provide the direct manipulation interface for
deforming and cutting operations.
 Simulate cutting and deforming operations
with force feedback.
 Implement a virtual modeling environment.

Introduction

Motivation
Physically based modeling and simulation is
desirable to increase reality.
 Problem：

Physically based models requires more computation cost than
geometrical models.
Hard to real-time!!

Solution:
Use two models of different complexity for physical and
geometric simulations.
Introduction

Background-1

Free Form Deformation

Free-Form Deformation of Solid Geometric Models; SIGGRAPH ’86, pp.151-161, 1986.
approach  can’t represent force
 Control-point based can’t direct operation
 Geometric

Direct Deformation Method

A Direct Deformation Method;
Proc. VRAIS’93, pp.499-504, 1993.
 Can’t
compute the
interaction force.
 Must combine other model
that can compute inter-force.
Introduction

Background-2

Combine physically based model
model  slow, hard to real-time
 Linear FEM model  bad for large deformation
 Spring-Network model  higher update rate
 Network of spring is constructed along edges of
the polygon model
 The result of the simulation is reflected on the
precise geometry model.
 FEM
Introduction

Main Idea




The shape of objects are defined
as a collection of tetrahedral elements.
Surface shape is represented by a geometric model
Physical reaction is simulated using a spring model.
The deformation of the spring model is reflected onto
the geometric model by using the interpolation
technique.
Deformation Operation

A spring network that covers a
cubic area is created.

spring cells that is out of the
object volume is deleted.

根據使用者操作算出作用於彈
簧模型上的力.Deform cells.

由幾何模型的內插方法Deform
objects.
Tearing Operation

根據施力計算spring
network 的變形量

受力超過彈簧承受值的端
點與邊便分開

根據spring network的狀況
分離代表object的四面體
並計算應有的形變量
Tearing Operation
Cutting Operation

Sculpturing operation

Galyean T.A.: Sculpting: An Interactive Volumetric Modeling Technique, Computer Graphics, vol.25, no.4, pp.267-274, 1991.

Voxel-based model was used to define the shape
Force feedback to the operator was determined only from the velocity of
cutting the object.



Geometrical cutting operation

Tanaka A., Hirota K., Kaneko T.: Virtual Cutting with Force Feedback; Proc. VRAIS ’98, pp.71-75, 1998.

Boolean operation on the polygon-based model
Force feedback :


Yamamoto K., Ishiguro A., Uchikawa Y.: A Development of Dynamic Deforming Algorithms for 3D Shape Modeling with
Generation of Interactive Force Sensation; Proc. VRAIS ’93, pp.505-511, 1993.
Our method



Coarse physical model and fine geometric model and combined
them with each other.
Fast update rate of physical simulation for force feedback
Precise representation of geometric shape
Cutting Operation

Sculpturing operation
Cutting Operation

Sculpturing operation
Cutting Operation

Sculpturing operation

Galyean T.A.: Sculpting: An Interactive Volumetric Modeling Technique, Computer Graphics, vol.25, no.4, pp.267-274, 1991.

Voxel-based model was used to define the shape
Force feedback to the operator was determined only from the velocity of
cutting the object.



Geometrical cutting operation

Tanaka A., Hirota K., Kaneko T.: Virtual Cutting with Force Feedback; Proc. VRAIS ’98, pp.71-75, 1998.

Boolean operation on the polygon-based model
Force feedback :


Yamamoto K., Ishiguro A., Uchikawa Y.: A Development of Dynamic Deforming Algorithms for 3D Shape Modeling with
Generation of Interactive Force Sensation; Proc. VRAIS ’93, pp.505-511, 1993.
Our method



Coarse physical model and fine geometric model and combined
them with each other.
Fast update rate of physical simulation for force feedback
Precise representation of geometric shape
Cutting Operation

Geometrical cutting operation




Boolean operation
Polygon model
Suppose object A and a locus of
cutting device B are defined.
The object after cutting is
represented by A AND (NOT B)
Cutting Operation

Geometrical cutting operation

Our objects of interest and the cutting device given in solid models are
all converted into a set of triangular patches with normal directions
indicating the external direction.
Cutting Operation

Geometrical cutting operation


Cutting friction increases in proportion to the velocity
of the cutting blade.
Checking whether all the polygons (triangles) interact
with the straight lines.


If no interaction, the force = 0
If an interaction exists,




be its present position
be its position at a cycle prior.
is a cycle and is set to be 1[ms]
k is a constant between force and
speed and is set to be 0:2N/(m/s)].
Cutting Operation

Geometrical cutting operation - result
Cutting Operation

Geometrical cutting operation - result
Cutting Operation

Geometrical cutting operation

Contribution



With the availability of the force feedback, cutting can be
performed more intuitively than with visual feedback alone.
The feedback of force may be used to reduce the effect of
sway and stabilize the cutting motion.
Future Work


Extend with a device with torque feedback. For the
representation of torque, we need to define the distribution of
force on the edge and sides of cutting tool.
The simulation of cutting soft materials that deform during the
operation.
Cutting Operation

Sculpturing operation

Galyean T.A.: Sculpting: An Interactive Volumetric Modeling Technique, Computer Graphics, vol.25, no.4, pp.267-274, 1991.

Voxel-based model was used to define the shape
Force fed back to the operator was determined only from the velocity of
cutting the object.



Geometrical cutting operation

Tanaka A., Hirota K., Kaneko T.: Virtual Cutting with Force Feedback; Proc. VRAIS ’98, pp.71-75, 1998.

Boolean operation on the polygon-based model
Force feedback :


Yamamoto K., Ishiguro A., Uchikawa Y.: A Development of Dynamic Deforming Algorithms for 3D Shape Modeling with
Generation of Interactive Force Sensation; Proc. VRAIS ’93, pp.505-511, 1993.
Our method



Coarse physical model and fine geometric model and combined
them with each other.
Fast update rate of physical simulation for force feedback
Precise representation of geometric shape
Cutting Operation
Computation of Cutting Force
 Geometric Cutting

Cutting Operation

Computation of Cutting Force


Define the cutting edge as
a finite set of discrete edges.
Each discrete edge holds the
position of two points.



One is the position where the cutting edge collides with the
deformed object.
The other is the position where the cutting edge collides with
the object in a non-deformed state.
Deformation of the object on each discrete edge is
calculated as the disparity between those positions.
Cutting Operation

Computation of Cutting Force




We assume that the force affecting on a discrete edge is
proportional to the displacement at the point where the
discrete edge collides with the object.
By computing the force on each discrete edge, we
obtain the approximate distribution of force on the edge.
Discrete edges are independent of each other.
Updating the position of the colliding point based on the
force affecting the discrete edge.
Cutting Operation

Computation of Cutting Force

Fractional force (摩擦力)



Cutting resistance (切割阻力)


Represent the friction between the cutting edge and the object.
Does not contribute to cutting
The part of the material is destroyed when the shearing force
exceed the maximum shearing force that the material can bear.
Viscous drag (黏滯曳力)

It is proportional to the velocity of the cutting edge.
Cutting Operation

Computation of Cutting Force

Operation of Cutting Tool:


Calculate force :




The position of the discrete cutting edge (Pi) is updated
according to the operation of the cutting tool by the user, and
the force on the edge is calculated.
Fractional force
Cutting resistance
Viscous drag
Feedback Force :
Calculate the force on each discrete edge as the sum of the
three forces discussed above
 The cutting edge moves toward Pi to the closest point

at which it can stably exist without cutting the material.
Cutting Operation

Geometric Cutting

The geometric change caused by the cutting
operation is represented by dividing tetrahedral
colliding with the trajectory of the cutting edge.

The proposed algorithm provides a fast method to
compute intersection between the cutting edge and
the object approximately.
Cutting Operation

Geometric Cutting

紀錄軌跡
分割三角形
分割物體
更新相鄰關係

The dividing patterns of each tetrahedron



Cutting Operation

Geometric Cutting

The shape consisting of 6000 tetrahedral is
colliding with the trajectory surface consisting
of 18 polygons and took about 4 seconds for
the geometric processing.
Conclusion


We proposed an approach to realize cutting and
deforming operations with force feedback.
We defined coarse physical model and fine geometric
model and combined them with each other.



fast update rate of physical simulation for force feedback
the precise representation of geometric shape
By sharing a geometric model in both cutting and
deforming operations, it became possible to switch
these two operations without the transforming the
internal representation of the object.